Strong magnetic fields of old white dwarfs are symmetric about the stellar rotation axes

Many magnetic white dwarfs exhibit a polarised spectrum that periodically varies as the star rotates because the magnetic field is not symmetric about the rotation axis. In this work, we report the discovery that while weakly magnetic white dwarfs of all ages with M < 1Mo show polarimetric variability with a period between hours and several days, the large majority of magnetic white dwarfs in the same mass range with cooling ages older than 2 Gyr and field strengths > 10 MG show little or no polarimetric variability. This could be interpreted as extremely slow rotation, but a lack of known white dwarfs with measured periods longer than two weeks means that we do not see white dwarfs slowing their rotation. We therefore suggest a different interpretation: old strongly magnetic white dwarfs do not vary because their fields are roughly symmetric about the rotation axes. Symmetry may either be a consequence of field evolution or a physical characteristic intrinsic to the way strong fields are generated in older stars. Specifically, a strong magnetic field could distort the shape of a star, forcing the principal axis of maximum inertia away from the spin axis. Eventually, as a result of energy dissipation, the magnetic axis will align with the angular momentum axis. We also find that the higher-mass strongly magnetised white dwarfs, which are likely the products of the merging of two white dwarfs, may appear as either polarimetrically variable or constant. This may be the symptom of two different formation channels or the consequence of the fact that a dynamo operating during a merger may produce diverse magnetic configurations. Alternatively, the massive white dwarfs with constant polarisation may be rotating with periods much shorter than the typical exposure times of the observations.